
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
There is a pile with  $15$  coins on a table. At each step, Pedro choses one of the piles in the table with  $a>1$  coins and divides it in two piles with  $b\geq1$  and  $c\geq1$  coins and writes in the board the product  $abc$ . He continues until there are  $15$  piles with  $1$  coin each. Determine all possible values that the final sum of the numbers in the board can have.

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