
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
If \[x \cdot \sqrt{x^2 - 1} + \frac{1}{x + \sqrt{x^2 - 1}} = 21,\] then find \[x^2 \cdot \sqrt{x^4 - 1} + \frac{1}{x^2 + \sqrt{x^4 - 1}}.\]

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