
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 binomial expansion of $(1 + 0.3)^{500}$:
\[
(1 + 0.3)^{500} = \sum_{k=0}^{500} \binom{500}{k} (0.3)^k = A_0 + A_1 + A_2 + \dots + A_{500},
\]
where $A_k = \binom{500}{k} (0.3)^k$ for $k = 0, 1, 2, \ldots, 500$. Determine for which $k$ is $A_k$ the largest.

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