
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 a sequence $\{a_n\}$ that satisfies $a_1=m$ $(m\in\mathbb{N}_+)$, $a_{n+1}=\begin{cases} \frac{a_n}{2}, & \text{if } a_n \text{ is even} \\ 3a_n+1, & \text{if } a_n \text{ is odd} \end{cases}$, if $a_6=1$, then all possible values of $m$ are __________.

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