
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 the function $f(x)$ on $\mathbb{R}$ such that $f(0)=0$, $f(x)+f(1-x)=1$, $f\left(\frac{x}{5}\right)=\frac{1}{2}f(x)$, and for $0 \leq x_1 < x_2 \leq 1$, $f(x_1) \leq f(x_2)$. Find the value of $f\left(\frac{1}{2007}\right)$.

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