
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 $f(x)$ is an odd function defined on $\mathbb{R}$, and for $x \geq 0$, $f(x) = a^x - 1$ ($a > 0$ and $a \neq 1$).

(1) Find the value of $f(2) + f(-2)$;  
(2) Find the expression for $f(x)$;  
(3) Solve the inequality $f(x) < 4$, and express the result as a set or interval.

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