
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
For a positive integer  $n$  that is not a power of two, we define  $t(n)$  as the greatest odd divisor of  $n$  and  $r(n)$  as the smallest positive odd divisor of  $n$  unequal to  $1$ . Determine all positive integers  $n$  that are not a power of two and for which we have  $n = 3t(n) + 5r(n)$ .

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