
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
Consider the expression $(1+0.15)^{500}$ expanded using the binomial theorem:
\[
(1+0.15)^{500} = \sum_{k=0}^{500} \binom{500}{k} (0.15)^k.
\]
Denote each term in the sum as $B_k = \binom{500}{k} (0.15)^k$ for $k = 0, 1, 2, \ldots, 500$. Determine the value of $k$ for which the term $B_k$ is the largest.

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