
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
Let \( c_{1}, c_{2}, \cdots \) be a sequence of positive integers such that for any positive integers \( m \) and \( n \) satisfying \( 1 \leqslant m \leqslant \sum_{i=1}^{n} c_{i} \), there exist positive integers \( a_{1}, a_{2}, \cdots, a_{n} \) such that
$$
m=\sum_{i=1}^{n} \frac{c_{i}}{a_{i}} .
$$

For each fixed \( i \) \(\left(i \in \mathbf{N}^{*}\right)\), find the maximum value of \( c_{i} \).

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