
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 hyperbola C, centered at the origin and symmetric about the coordinate axes, intersects with the circle O: x<sup>2</sup>+y<sup>2</sup>=5 at the point P(1, -2). The tangent line to the circle O at point P is parallel to one of the asymptotes of the hyperbola C. Find the length of the real axis of the hyperbola.

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