
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 circle $C$: $(x)^2+(y)^2+4x-6y-3=0$.
(1) Find the equation of the tangent line to circle $C$ passing through point $M(-6,-5)$;
(2) A line passing through point $N(1,3)$ intersects circle $C$ at points $A$ and $B$. Find the maximum area of $\triangle ABC$.

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