
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]


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Let \( A(x_{1}, y_{1}) \) and \( B(x_{2}, y_{2}) \) be two points on the curve \( C: x^{2}-y^{2}=2 \) (where \( x > 0 \)). Then the minimum value of \( f = \overrightarrow{OA} \cdot \overrightarrow{OB} \) is ______.

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