
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
In the Cartesian coordinate system, the coordinates of the vertices of triangle $ABC$ are as follows: $A(0, 4)$; $B(-3, 0)$, $C(1, 1)$.

(1) Calculate the distance from point $C$ to the line $AB$.
(2) Find the equation of the line representing the altitude from point $B$ to side $AC$.

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