
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 a function $f(x)$ on $\mathbb{R}$ such that
$$
f(x) = \begin{cases}
\log_{2}(8-x) & \text{if } x \leq 0, \\
f(x-1) - f(x-2) & \text{if } x > 0.
\end{cases}
$$
Determine the value of $f(2013)$.

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