
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
Integers a, b, c, d, and e satisfy the following three properties: 
(i)  $2 \le a < b <c <d <e <100$  
(ii) $ \gcd (a,e) = 1 $ (iii) a, b, c, d, e form a geometric sequence. 
What is the value of c?

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