
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
Find the value of $S_{20}$, given that for a sequence ${a_n}$ with its first $n$ terms sum $S_n$, it is known that for any $n\in \mathbb{N}^*$, $2S_n=n^2+a_n$.

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