
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 $x$, $y$, and $z$ representing different lines or planes in space, among the following conditions, identify which one ensures the truth of the proposition "If $x \perp z$, and $y \perp z$, then $x \parallel y$". Fill in the correct condition code.
1. $x$, $y$, $z$ are lines;
2. $x$, $y$, $z$ are planes;
3. $x$, $y$ are lines, $z$ is a plane;
4. $x$ is a line, $y$, $z$ are planes.

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