
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 the coordinates of the three vertices of $\triangle ABC$ as $A(0,5)$, $B(1,-2)$, and $C(-6,4)$, find the equation of the line containing the altitude drawn from point $C$ to side $BC$.
(2) Given the equation of line $l$ as $(a-1)x + y - 2 - a = 0, (a \in \mathbb{R})$, find the equation of line $l$ if its intercepts on both coordinate axes are equal.

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