
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 the coordinates of the three vertices of triangle $\triangle ABC$ as $A(1,1)$, $B(3,2)$, and $C(5,4)$:
(1) Find the equation of the line containing the altitude from $AB$.
(2) Suppose line $l$ is parallel to $AC$, and the intercept on the $x$-axis is 1 unit greater than that on the $y$-axis, find the perimeter of the triangle formed by line $l$ and the two coordinate axes.

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