
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
A triangle has three sides of the following lengths: \(8\), \(11\), and \(x^2\). What are all the positive integer values of \(x\) such that the triangle exists? Separate your answers using commas and express them in increasing order.

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