
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
We define the weight  $W$  of a positive integer as follows:  $W(1) = 0$ ,  $W(2) = 1$ ,  $W(p) = 1 + W(p + 1)$  for every odd prime  $p$ ,  $W(c) = 1 + W(d)$  for every composite  $c$ , where  $d$  is the greatest proper factor of  $c$ .  Compute the greatest possible weight of a positive integer less than 100.

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