
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 triangular pyramid P-ABC, D is the midpoint of PA, O is the centroid of triangle ABC. There are four statements given below:

1. $OD \parallel$ plane PBC
2. $OD \perp PA$
3. $OD \perp BC$
4. $PA = 2OD$

Identify the correct statements.

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