
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 a triangular pyramid \( A B C D \) where the angles \( B D C, C D A \), and \( A D B \) are all right angles, and \( D A = a \), \( D B = b \), \( D C = c \). Point \( M \), which belongs to the face \( A B C \), is equidistant from the planes of all other faces of the pyramid. Calculate the length of the segment \( D M \).

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