
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 an odd function $f(x)$ on $\mathbb{R}$, where for $x \geqslant 0$, $f(x)=\begin{cases} & \log_{2}(x+1), & x\in [0,1) \\ & |x-3|-1, & x\in [1,+\infty ) \end{cases}$. Then, find the sum of all zeros of the function $F(x)=f(x)-a$, where $-1 < a < 0$.

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