
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 given problem, we have a regular tetrahedron \(ABCD\) with edge length 1. \(M\) is the midpoint of \(AC\), and \(P\) is a point on the line segment \(DM\). What is the minimum value of \(AP + BP\)?

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