
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 sum of the first n terms of a geometric sequence {a_n} is S_n. It is known that a_2a_5 = 2a_3, and the arithmetic mean of a_4 and 2a_7 is 5/4. Then calculate S_5.

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