
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
A plane is given parametrically by:
\[\mathbf{v} = \begin{pmatrix} 2 + 2s - t \\ 1 + 2s \\ 4 - s + 3t \end{pmatrix}.\]
Find the equation of this plane in the form:
\[Ax + By + Cz + D = 0,\]
where $A$, $B$, $C$, $D$ are integers, $A > 0$, and $\gcd(|A|, |B|, |C|, |D|) = 1.$

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