
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]


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Given a circle $C$ that passes through point $P(1,1)$ and is symmetric to circle $M$: $(x+2)^{2}+(y+2)^{2}=r^{2}(r > 0)$ about the line $x+y+2=0$.

(1) Find the standard equation of circle $C$;

(2) Let $Q$ be a moving point on circle $C$, find the minimum value of $\overrightarrow{PQ} \cdot \overrightarrow{MQ}$;

(3) Two distinct lines are drawn through point $P$ intersecting circle $C$ at points $A$ and $B$ respectively. The slopes of line $PA$ and line $PB$ are complementary angles, $O$ is the coordinate origin, determine whether line $OP$ and line $AB$ are parallel. Please explain your reasoning.

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