
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 hyperbola has its center at the origin, with axes of symmetry coinciding with the coordinate axes. If its asymptotes are perpendicular to each other, find the eccentricity of the hyperbola.

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