
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
The sequence \(\left(x_{n}\right)\) is defined by the conditions:

\[ x_{1}=a, \quad x_{n+1}=x_{n}^{2} \]

Find all values of \(a\) for which the sequence is periodic.

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