
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
Given a positive integer \( n \) and a sequence of real numbers \( a_{1}, a_{2}, \cdots, a_{n} \) such that for each \( m \leq n \), it holds that \( \left|\sum_{k=1}^{m} \frac{a_{k}}{k}\right| \leq 1 \), find the maximum value of \( \left|\sum_{k=1}^{n} a_{k}\right| \).

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