
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 point $P(-5,0)$, point $Q$ is a point on the circle $(x-5)^{2}+y^{2}=36$, and $M$ is the midpoint of segment $PQ$.
(I) Find the equation of the trajectory $C$ of point $M$.
(II) The line $l$ passing through point $P$ intersects the trajectory $C$ at two distinct points $A$ and $B$. (a) If $|AB|=4$, find the equation of line $l$. (b) Find the value of $\overrightarrow{PA} \cdot \overrightarrow{PB}$.

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