
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 periodic sequence $\left\{x_{n}\right\}$ that satisfies $x_{n}=\left|x_{n-1}-x_{n-2}\right|$ for $n \geqslant 3$ and $x_{1}=1$, $x_{2}=a \geqslant 0$, determine the sum of the first 2002 terms of the sequence when the period is minimal.

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