
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 parametrically described by
\[\mathbf{u} = \begin{pmatrix} 2 + 2s + 3t \\ 4 + 2s - t \\ 1 - 3s - t \end{pmatrix}.\] Determine the equation of the 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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