
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 lines $l\_1$: $2x+3y-5=0$, $l\_2$: $x+2y-3=0$ intersect at point $P$, and line $l\_3$: $2x+y-5=0$
(1) Find the equation of the line that passes through point $P$ and is parallel to $l\_3$;
(2) Find the equation of the line that passes through point $P$ and is perpendicular to $l\_3$.

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