
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) \(2 \leq a<b<c<d<e<100\)
(ii) \(\operatorname{gcd}(a, e)=1\)
(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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