
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 points $O$ and $F(-2,0)$ are the center and left focus of the hyperbola $\frac{x^{2}}{a^{2}}-y^{2}=1 (a > 0)$, respectively. Let $P$ be any point on the right branch of the hyperbola. Determine the range of values for $\overrightarrow{OP} \cdot \overrightarrow{FP}$.

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