
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
\[\mathbf{v} = \begin{pmatrix} 2 + 2s - 3t \\ 4 - 2s \\ 5 + s + 3t \end{pmatrix}.\]
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