
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
Suppose that \( f(x) \) is a function defined for every real number \( x \) with \( 0 \leq x \leq 1 \) with the properties that

- \( f(1-x)=1-f(x) \) for all real numbers \( x \) with \( 0 \leq x \leq 1 \),
- \( f\left(\frac{1}{3} x\right)=\frac{1}{2} f(x) \) for all real numbers \( x \) with \( 0 \leq x \leq 1 \), and
- \( f(a) \leq f(b) \) for all real numbers \( 0 \leq a \leq b \leq 1 \).

What is the value of \( f\left(\frac{6}{7}\right) \) ?

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