
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
Find the equation of the plane passing through points \( (2, -1, 0) \), \( (0, 3, 1) \), and that is perpendicular to the plane given by \( 2x - y + 4z = 7 \). Represent 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}
user