
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
Given a geometric sequence with positive terms \{a_n\} and the sum of the first n terms denoted as S_n, and it's known that a_1a_6=2a_3, and the arithmetic mean of a_4 and a_6 is 5, find the value of S_5.

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