
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
Define an odd function $f(x)$ on the interval \([-1, 1]\) with the smallest positive period being 2. When \(0 < x < 1\), $f(x)$ is equal to $$\frac{2^x}{4^x + 1}$$.
(1) Discuss the monotonicity of $f(x)$ on the interval \((0, 1)\);
(2) Determine the expression for $f(x)$ on the interval \([-1, 1]\);
(3) The function $y = f(x) - a$ has a zero point, find the range of the real number $a$.

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