
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 circle C: $x^2+y^2+4x-2y+a=0$, and a line $l: x-y-3=0$, with point O being the origin of the coordinates.
(1) Find the equation of line $m$ that passes through the center of circle C and is perpendicular to line $l$;
(2) If line $l$ intersects circle C at points M and N, and $OM \perp ON$, find the value of the real number $a$.

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