
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]


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Given that point P is outside the plane of the parallelogram ABCD, if $$\overrightarrow {AB}$$\=(2，-1，-4), $$\overrightarrow {AD}$$\=(4，2，0), $$\overrightarrow {AP}$$\=(-1，2，-1). Determine the correct statement(s) among the following:
① AP ⊥ AB;
② AP ⊥ AD;
③ $$\overrightarrow {AP}$$ is the normal vector of plane ABCD;
④ $$\overrightarrow {AP}$$ ∥ $$\overrightarrow {BD}$$.

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