
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 an arithmetic sequence ${a_n}$ with the sum of its first $n$ terms being $S_n$, $a_1$ = -2, and the common difference $d$ ($d \in \mathbb{N}^*$).
(1) If $a_5$ = 30, find the general term formula of the sequence ${a_n}$;
(2) Determine if there exist $d$ and $n$ such that $S_n$ = 10. If they exist, find all possible values of $d$ and $n$, and derive the general term formula of the sequence ${a_n}$; if not, explain the reason.

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