
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
Compose the equation of the plane that contains the line $\frac{x-1}{2}=-\frac{y}{3}=3-z$ and is parallel to the line of intersection of the planes $4 x+5 z-3=0$ and $2 x+y+2 z=0$.

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