
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 sum of the first $n$ terms of the sequence $\{a_{n}\}$ is $S_{n}$, and $\{a_{n}\}$ satisfies $2a_{n+1}=a_{n}+a_{n+2}$, $a_{5}-a_{3}=2$, and $S_{2}=2$, determine the value of $a_{9}$.

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