
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 $f(x)$ on $\mathbb{R}$ defined as
$$
f(x)= 
\begin{cases} 
\log_{2}^{(3-x)} & \text{if } x\leq 0\\
f(x-1)-f(x-2) & \text{if } x>0
\end{cases}
$$
find the value of $f(2017)$.

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