
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
A circle $O: x^2 + y^2 = 1$ with the center at the origin $O$ is given. A point $P(x, y)$ lies on the line $x - y - 2 = 0$. A tangent line $PQ$ to the circle at point $P$ is drawn such that $\angle OPQ = 30^\circ$, find the value(s) of $x$.

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