
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 an infinite arithmetic sequence ${a_n}$ is $S_n$, and it is known that $a_1=1$, $S_3=12$.
(1) Find the values of $a_{24}$ and $S_{7}$;
(2) If both $m$ and $n$ are positive integers and satisfy $a_{m}=S_{n}$, find the set of all possible values of $n$.

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