In this passage about cultural identity, choose the adverb or adjective that best completes the phrase: “open to external influences but holding its roots _______.”

Introduction / Context:
This final cloze item in the cultural passage completes the tree metaphor. The culture is described as “open to external influences but holding its roots _______.” The missing word should reinforce the idea that, although the culture accepts outside ideas, it still firmly holds on to its core traditions and values.

Given Data / Assumptions:

1) The phrase to complete is “holding its roots _______.”
2) The options are: light, fast, hardly, hard.
3) The context is a tree (or culture) that remains firmly rooted while being open to external influences.
4) We need a word that expresses firmness or strength of grip.
5) The sentence is metaphorical but should still sound natural in English.

Concept / Approach:
In English, we use “hold hard”, “hold fast” and “hold firmly” to indicate a strong and determined grip. In this multiple choice set, “hard” is the best fit for conveying firmness in a simple way. “fast” could have worked in the phrase “hold fast”, but “holding its roots fast” is less common and feels slightly archaic. “hardly” changes the meaning completely, and “light” is the opposite of what is intended.

Step-by-Step Solution:
Step 1: Focus on the idea: the culture is receptive to outside influences but still firmly anchored in its own roots. Step 2: Test “light”: “holding its roots light” does not make sense; light refers to weight, not firmness. Step 3: Test “fast”: “holding its roots fast” is an old fashioned but possible phrase; however, we usually see “hold fast” as a verb phrase, not “holding its roots fast” in modern prose. Step 4: Test “hardly”: “holding its roots hardly” would mean “holding its roots scarcely”, which is the opposite of firm holding. Step 5: Test “hard”: “holding its roots hard” clearly suggests holding firmly, especially in the simple vocabulary often used in exam passages. Step 6: Given the options, “hard” is the closest to the intended meaning of strong attachment.

Verification / Alternative check:
Read the complete metaphor: “It has grown just like a tree, open to external influences but holding its roots hard.” The two halves now form a neat contrast: openness above ground, firmness below ground. The reader understands that the culture is flexible on the surface but deeply rooted in its own heritage. None of the other options captures this balance as clearly.

Why Other Options Are Wrong:
“light” suggests the opposite of strength or firmness and therefore contradicts the metaphor of deep roots. “fast” might tempt some readers because of the phrase “hold fast”, but in this exact position and with this set of options, “hard” is more straightforward and modern. “hardly” means “barely” or “almost not”, which would wrongly suggest that the culture scarcely holds to its roots.

Common Pitfalls:
One pitfall is to overvalue archaic or poetic expressions like “hold fast” and therefore choose “fast” automatically, without checking the full sentence and style. Another is misunderstanding “hardly” as related to “hard” in the sense of strong; in fact, “hardly” has the opposite meaning. Always be cautious with adverbs ending in “ly”, and test the sentence logically before deciding.

Final Answer:
The word that best completes the sentence is hard.