
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
Given the line

$$
\begin{aligned}
3x - 2y - z + 4 &= 0 \\
x - 4y - 3z - 2 &= 0
\end{aligned}
$$

find its projection onto the plane

$$
5x + 2y + 2z - 7 = 0.
$$

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