
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
Luca has four ropes whose lengths are 42 inches, 56 inches, 63 inches, and 77 inches. He wants to cut the ropes into equal length pieces for crafting, with no rope being wasted. What is the greatest number of inches possible in the length of each piece?

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