
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 $f(x)$ with a domain of $R$ satisfying $f(1+x)=f(1-x)$, $f(1-x)=1-f(x)$, and on the interval $[0,1]$, it also satisfies: ① $f(x_1) \leq f(x_2)$ when $x_1 < x_2$; ② $f(0)=0$; ③ $f(\frac{x}{3})=\frac{1}{2}f(x)$. Evaluate $f(-\frac{5}{3})+f(\frac{1}{8})$.

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