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

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