
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<sub>1</sub> and F<sub>2</sub> are two foci of a hyperbola C, P is a point on C, and ∠F<sub>1</sub>PF<sub>2</sub>=60°, |PF<sub>1</sub>|=λ|PF<sub>2</sub>| (λ>1), and the eccentricity of C is (√7)/2, find the value of λ.

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