
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 any triangle  $ABC$  and any positive integer  $n$ , we say that  $n$  is a *decomposable* number for triangle  $ABC$  if there exists a decomposition of the triangle  $ABC$  into  $n$  subtriangles with each subtriangle similar to   $\triangle ABC$ . Determine the positive integers that are decomposable numbers for every triangle.

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