
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
Let $M=2^t+i_{t-1}\times2^{t-1}+\ldots+i_1\times2+i$, where $i_k=0$ or $1$ ($k=0,1,2,\ldots,t-1,t\in\mathbb{N}^+$), and denote $M=(1i_{t-1}i_{t-2}\ldots i_1i)_2$. For a given $x_1=(1i_{t-1}i_{t-2}\ldots i_1i)_2$, construct an infinite sequence $\{x_n\}$ as follows: $x_2=(1ii_{t-1}i_{t-2}\ldots i_2i_1)_2$, $x_3=(1i_1ii_{t-1}\ldots i_3i_2)_2$, $x_4=(1i_2i_1ii_{t-1}\ldots i_3)_2\ldots$,
1. If $x_1=109$, then $x_3=$    (Answer in digits);
2. Given a positive integer $m$, if $x_1=2^{2m+2}+2^{2m+1}+2^{2m}+1$, then the smallest value of $n$ for which $x_n=x_1$ ($n\in\mathbb{N}^+$ and $n\neq1$) is    .

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