
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
The function $f(x)$ is defined as follows:
\[f(x)= \begin{cases} \log_{2}(2^{x}-8),& \text{if } x > 3 \\ f(x+2), & \text{if } x \leqslant 3 \end{cases}\]
Find $f(0)=$ \_\_\_\_\_\_.

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