
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 a line $l$ that passes through the point $M(1,1)$ and is parallel to the line $2x+4y+9=0$:
1. Find the equation of line $l$.
2. If line $l$ intersects the circle $x^2+y^2+x-6y+m=0$ at points $P$ and $Q$, with $O$ being the origin and $OP \perpendicular OQ$, find the value of the real number $m$.

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