
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
Two triangular pyramids \( MABC \) and \( NABC \) have a common base and no other common points. All vertices of both pyramids lie on the same sphere. Find the lengths of the edges \( MA \) and \( MB \) if it is known that they are equal to each other, and the lengths of all other edges of these pyramids are \( \sqrt{3} \).

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