
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 C: x^{2}-y^{2}=2, and point P is on C with |PF_{1}|=2|PF_{2}|, calculate cos ∠F_{1}PF_{2}.

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