
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 a function $f(x)$ for any real numbers $x$, $y$ satisfies $f(xy)=f(x)\cdot f(y)$, and $f(-1)=1$, $f(27)=9$. When $0 \leqslant x < 1$, $0 \leqslant f(x) < 1$.
1. Determine the parity of $f(x)$;
2. Determine the monotonicity of $f(x)$ on $[0,+\infty)$ and provide a proof;
3. If $a \geqslant 0$ and $f(a+1) \leqslant 39$, find the range of $a$.

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