
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
Let line $l: 3x+4y+a=0$, and circle $C: (x-2)^{2}+y^{2}=2$. If there exists a point $M$ on line $l$ such that the tangents $MP$ and $MQ$ ($P,Q$ are the points of tangency) from $M$ to circle $C$ satisfy $\angle PMQ=90^{\circ}$, determine the range of values for $a$.

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