
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 center of the hyperbola $\Gamma$ is at the origin, and its foci are on the coordinate axes. The real axis of $\Gamma$ is 4, and one of its asymptotes is $y=2x$. Find the standard equation of the hyperbola $\Gamma$.

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