
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 expansion of \( (1 + 0.3)^{500} \) using the binomial theorem without any simplification. The terms of the expansion are given by:
\[
A_k = {500 \choose k}(0.3)^k, \text{ for } k = 0, 1, 2, \ldots, 500.
\]
Determine for which \( k \) the term \( A_k \) is the largest.

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