
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 equation of the hyperbola that shares the same foci with the ellipse $\dfrac{{{x}^{2}}}{4}+{{y}^{2}}=1$ and passes through the point $P(2,1)$ must be expressed in the form $\dfrac{{{x}^{2}}}{a}-\dfrac{{{y}^{2}}}{b}=1$, where $a$ and $b$ are constants to be determined.

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