
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 $n \in \mathbb{N}^*$, $a_{n+T} = a_n$, then $\{a_n\}$ is called a periodic sequence, and $T$ is called its period. It is known that the sequence $\{x_n\}$ satisfies $x_1 = 1$, $x_2 = a$ ($a \leq 1$), $x_{n+2} = |x_{n+1} - x_n|$, when the period of the sequence $\{x_n\}$ is 3, then the sum of the first 2013 terms of $\{x_n\}$, $S_{2013} =$ .

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