
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
Find the equation of the plane passing through the points \( (1, 4, -3) \) and \( (0, -3, 0) \), and containing the line
\[ \frac{x - 2}{4} = \frac{y + 2}{-1} = \frac{z - 1}{5}.\]
Express your answer in the form
\[ Ax + By + Cz + D = 0, \]
where \( A, B, C, D \) are integers, \( A > 0 \), and \( \text{gcd}(|A|, |B|, |C|, |D|) = 1 \).

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