
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 $\left\{a_n\right\}$ is an arithmetic sequence, and $a_1+a_3=8, a_2+a_4=12,$

(1) Find the general formula for the sequence $\left\{a_n\right\}$;

(2) Let the sum of the first $n$ terms of $\left\{a_n\right\}$ be $S_n$. If $S_n=420$, find the value of the positive integer $n$.

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