
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 $f(x) = \begin{cases} \log_{2}(3-x), & x \leq 0 \\ f(x-1) - f(x-2), & x > 0 \end{cases}$. Find the value of $f(11)$.

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