
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 that $a$ is a line, and $\alpha$, $\beta$ are two different planes, the following statements are provided:
① $a \perp \alpha$;
② $a \perp \beta$;
③ $\alpha \parallel \beta$.
Determine the number of true propositions formed by using any two of the above statements as premises and the remaining one as the conclusion.

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