
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
If point $O$ and point $F(-2,0)$ are the center and the left focus of the hyperbola $\frac{x^2}{a^2} - y^2 = 1 \; (a > 0)$, respectively, and point $P$ is 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