
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 function $y=f(x)$ ($x \neq 0$) is an odd function, and it is increasing when $x \in (0, +\infty)$. If $f(-1) = 0$, and $f\left(a- \frac{1}{2}\right) < 0$,  
(1) Find the value of $f(1)$;  
(2) Determine the range of the real number $a$.

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