
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
Let there be a conic section $C$ centered at the origin, with the coordinate axes as its axes of symmetry, an eccentricity of $\sqrt{2}$, and passing through the point $(5,4)$. Calculate its focal length.

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