
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
In the 2012 Liaoning college entrance examination, it is known that the geometric sequence $\{a_n\}$ is increasing, and $a = a_{10}$, $2(a_n + a_{n+2}) = 5a_{n+1}$. Find the general formula for the $n$-th term of the sequence $\{a_n\}$, denoted as $a_n = \_\_\_\_\_\_\_\_$.

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