
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 $\{a\_n\}$ where all terms are positive integers, for $n=1$, $2$, $3$, $...$, we have $a_{n+1}= \begin{cases}3a_{n}+5 & a_{n}\text{ is odd} \\\\ \frac {a_{n}}{2^{k}} & a_{n}\text{ is even. }{where }k\text{ is the positive integer making }a_{n+1}\text{ odd}\end{cases}$, when $a_{1}=11$, $a_{100}=$ _______ ; If there exists $m∈N^{*}$, when $n > m$ and $a_{n}$ is odd, $a_{n}$ is always a constant $p$, then the value of $p$ is _______ .

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