
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
Given the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \ (a > 0, b > 0)$, $P(2,2)$ is a point on the hyperbola, and the distance from the foci to its asymptotes is equal to the length of the real axis. Find the equation of this hyperbola.

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