
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
Let $\alpha$, $\beta$, and $\gamma$ be three distinct planes with $l$ being a line. Consider the following statements:
1. If $\alpha \parallel \beta$ and $\alpha \perpendicular \gamma$, then $\beta \perpendicular \gamma$.
2. If $\alpha \perpendicular \gamma$ and $\beta \perpendicular \gamma$, and $\alpha \cap \beta = l$, then $l \perpendicular \gamma$.
3. If a line $l$ is perpendicular to countless lines within the plane $\alpha$, then the line $l$ is perpendicular to the plane $\alpha$.
4. If there exist three non-collinear points within plane $\alpha$ that are equidistant from plane $\beta$, then plane $\alpha$ is parallel to plane $\beta$.

Identify the true statement(s) from the above (Write down the number(s) of all true statements).

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