
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
A function $f(x)$ defined on $\mathbb{R}$ satisfies $f(0)=0$, $f(x)+f(1-x)=1$, $f(\frac{x}{5})=\frac{1}{2}f(x)$, and $f(x_1)\leqslant f(x_2)$ when $0\leqslant x_1 < x_2\leqslant 1$. Find the value of $f(\frac{1}{2007})$.

A) $\frac{1}{2}$
B) $\frac{1}{16}$
C) $\frac{1}{32}$
D) $\frac{1}{64}$

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