
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 first, second, and third terms of a geometric sequence are distinct and equal to the second, fourth, and seventh terms of an arithmetic sequence, respectively. The product of these three numbers is 64. Find the first term of the geometric sequence.

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