
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
Using the binomial theorem to expand \((1 + 0.3)^{500}\), the expression can be written as
\[
{500 \choose 0}(0.3)^0 + {500 \choose 1}(0.3)^1 + {500 \choose 2}(0.3)^2 + \cdots + {500 \choose 500}(0.3)^{500} = B_0 + B_1 + B_2 + \cdots + B_{500},
\]
where \( B_k = {500 \choose k}(0.3)^k \) for \( k = 0, 1, 2, \ldots, 500 \). For which \( k \) is \( B_k \) the largest?

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