
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
Let $F$ be the right focus of the hyperbola $Γ$: $x^{2}- \frac{y^{2}}{4}=1$. A point $P$ on the right branch of $Γ$ is at a distance of $2$ from one asymptote, and there exists a point $Q$ on the other asymptote such that $\overrightarrow{FP}=λ \overrightarrow{PQ}$. Determine the value of $λ$.

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