
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 point $P$ on the line $x+y=0$ is used to draw two tangent lines $l\_1$ and $l\_2$ to the circle $C: (x+1)^{2}+(y-5)^{2}=2$. Points $A$ and $B$ are the points of tangency. When $CP$ is perpendicular to the line $y=-x$, find the measure of $\angle APB$.

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