
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 that $F\_1$ and $F\_2$ are the left and right foci of the hyperbola $x^{2}- \frac{y^{2}}{4}=1$, respectively. If there exists a point $P$ on the right branch of the hyperbola such that $( \overrightarrow{OP}+ \overrightarrow{OF_{2}}) \cdot \overrightarrow{F_{2}P}=0$ and $|PF_{1}|=λ|PF_{2}|$, determine the value of $λ$.

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