
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
In the arithmetic sequence $\{ a_{n} \}$:
$(1)$ Given $a_{5}=-1,a_{8}=2$, find $a_{1}$ and $d$;
$(2)$ Given ${a}_{m}=n,{a}_{n}=m,(m,n\in \mathbb{N}^{\ast},m\neq n)$ find $({a}_{m+n})$

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