
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
Let \( f(x) = a_{0} + a_{1} x + a_{2} x^{2} + \ldots + a_{n} x^{n} \), where \( a_{i} \) are nonnegative integers for \( i = 0, 1, 2, \ldots, n \). If \( f(1) = 21 \) and \( f(25) = 78357 \), find the value of \( f(10) \).

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