
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 $f(x)$ defined on the interval $[0, 1]$ such that it satisfies the following conditions:
1. $f(0)=0$;
2. $f(x) + f(1-x) =1$;
3. $f\left(\frac{x}{3}\right) = \frac{1}{2}f(x)$;
4. For any $0 \leq x_1 < x_2 \leq 1$, it holds that $f(x_1) \leq f(x_2)$.

Calculate $f\left(\frac{1}{2016}\right)$.

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