
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 a parametric expression of a plane,
\[\mathbf{v} = \begin{pmatrix} 2 + 2s - 3t \\ 4 + s \\ 1 - 3s + 4t \end{pmatrix},\]
find the equation of the plane. Write your answer in the form
\[Ax + By + Cz + D = 0,\]
where \(A\), \(B\), \(C\), and \(D\) are integers such that \(A > 0\) and \(\gcd(|A|,|B|,|C|,|D|) = 1\).

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