
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 tetrahedron \(ABCD\), all of whose faces are similar right-angled triangles with acute angles at vertices \(A\) and \(B\). The edge \(AB\) is equal to 1. Find the length of the shortest edge of the tetrahedron.

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