
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 that passes through the point (2,1) and has asymptotes tangent to the circle x^2 + (y - 2)^2 = 1 has the standard equation of \frac{{{x}^{2}}}{a}-\frac{{{y}^{2}}}{b}=1.

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