
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
The lengths of all six edges of a tetrahedron are integers, and the lengths of five of the edges are 14, 20, 40, 52, and 70. Determine the number of possible lengths for the sixth edge.

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