
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 $f(x)$ whose domain is $D$, if for any $x_1, x_2 \in D$, it holds that $f(x_1) \leq f(x_2)$ whenever $x_1 < x_2$, then the function $f(x)$ is called a non-decreasing function on $D$. Suppose $f(x)$ is a non-decreasing function on the interval $[0,1]$ and satisfies the following three conditions:
1. $f(0) = 0$;
2. $f\left(\frac{x}{3}\right) = \frac{1}{2}f(x)$;
3. $f(1-x) = 1-f(x)$.

Find the value of $f(1) + f\left(\frac{1}{2}\right) + f\left(\frac{1}{3}\right) + f\left(\frac{1}{6}\right) + f\left(\frac{1}{7}\right) + f\left(\frac{1}{8}\right)$.

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