
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
A sequence of natural numbers  $c_1, c_2,\dots$  is called *perfect* if every natural
number  $m$  with  $1\le m \le c_1 +\dots+ c_n$  can be represented as $m =\frac{c_1}{a_1}+\frac{c_2}{a_2}+\dots+\frac{c_n}{a_n}$ Given  $n$ , find the maximum possible value of  $c_n$  in a perfect sequence  $(c_i)$ .

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