
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the binomial expansion of \\((x^{2}+ \frac{1}{2 \sqrt {x}})^{n}\\) where \\(n \in \mathbb{N}^*\\), the sum of the first three binomial coefficients is 56. Determine the constant term of the expansion.

A) \\(\frac{45}{256}\\)
B) \\(\frac{47}{256}\\)
C) \\(\frac{49}{256}\\)
D) \\(\frac{51}{256}\\)

Present the answer in LaTex format: \boxed{Your answer}
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