
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 $\frac{x^{2}}{4}-\frac{y^{2}}{3}=1$, the ratio of the distance from a point \( P \) on the right branch to the left focus \( F_{1} \) and the distance to the right focus \( F_{2} \) is \( 2:1 \). Find the distance \( |OP| \).

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