
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 the function $f(x)=ax^{2}+x-a$, where $a \in \mathbb{R}$:
$(1)$ Solve the inequality $f(x) > 1$ when $a=2$;
$(2)$ If the function $f(x)$ has a maximum value of $\frac{17}{8}$, find the value of the real number $a$.

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