
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 that the geometric sequence $\{a_n\}$ is an increasing sequence, and $a_5^2 = a_{10}$, $2(a_n+a_{n+2})=5a_{n+1}$, determine the general formula for the sequence $\{a_n\}$.

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