
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
Let the sequence $\left\{a_{n}\right\}$ satisfy $a_{1}=a, a_{2}=b, 2a_{n+2}=a_{n+1}+a_{n}$. If $\lim _{n \rightarrow \infty}\left(a_{1}+a_{2}+\cdots+a_{n}\right)=4$, find the values of $a$ and $b$.

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