
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
If $\alpha$ and $\beta$ are distinct lines, and $\alpha \parallel \beta$, and $\gamma$ is a distinct plane such that $\alpha \perp \gamma$, determine the number of true propositions when one of $\alpha$, $\beta$, or $\gamma$ remains unchanged as a plane or a line.

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