
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
In the regular tetrahedron $P-ABC$, $D$ and $E$ are the midpoints of $AB$ and $BC$, respectively. Among the following statements: ① $AC \perp PB$; ② $AC \parallel$ plane $PDE$; ③ $AB \perp$ plane $PDE$, the correct statement(s) is/are \_\_\_\_\_\_\_\_.

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