
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 \\(x^{2}-y^{2}=1\\), with points \\(F_{1}\\) and \\(F_{2}\\) as its two foci, and point \\(P\\) on the hyperbola. If \\(PF_{1}\\) is perpendicular to \\(PF_{2}\\), then the value of \\(|PF_{1}|+|PF_{2}|\\) is \_\_\_\_\_\_.

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