
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 $\Gamma: x^{2}-y^{2}=1$ with a point $M$ in the first quadrant, a tangent line $l$ is drawn through $M$ to $\Gamma$, intersecting the asymptotes of $\Gamma$ at points $P$ and $Q$ (with $P$ in the first quadrant). Point $R$ is on the same asymptote as $Q$. If $\overrightarrow{R P} \cdot \overrightarrow{R Q} \geqslant a$ always holds, what is the range of values for $a$?

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