
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 $M(3,0)$, two lines $l_{1}$: $2x-y-2=0$ and $l_{2}$: $x+y+3=0$.
(1) Find the equation of line $l$ that passes through point $M$, intersects lines $l_{1}$ and $l_{2}$ at points $P$ and $Q$ respectively, and line segment $PQ$ is bisected by $M$.
(2) Find the equation of line $l_{3}$, which is the reflection of line $l_{1}$ about line $l_{2}$.

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