
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
(1) Given a line $m$ passes through the point $(2,4)$ and is perpendicular to two parallel lines $x-y+1=0$ and $x-y+2=0$, find the equation of line $m$.

(2) If a line $l$ passes through the point $(2,4)$ and the midpoint of the segment intercepted by the two parallel lines $x-y+1=0$ and $x-y+2=0$ lies on the line $x+2y-3=0$, find the equation of line $l$.

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