
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
Six numbers are written in a row. It is known that among them there is one unit and any three consecutive numbers have the same arithmetic mean. Find the maximum value of the geometric mean of any three consecutive numbers in this row if the arithmetic mean of all 6 numbers is A.

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