
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
In the sequence $\{a_n\}$, if there exists a certain positive integer $T$ such that for any $n\in N^*$, $a_{n+T}=a_{n}$ holds, then $\{a_n\}$ is called a periodic sequence, and $T$ is its period. Given that sequence $\{x_n\}$ satisfies $x_1=1$, $x_2=a(a\leqslant 1)$, $x_{n+2}=|x_{n+1}-x_n|$, and the period of sequence $\{x_n\}$ is $3$, the sum of the first $100$ terms of $\{x_n\}$ is ______.

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