
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 that $a > 0$ and $a \neq 1$, the function $f(x) = \begin{cases} \log_{\frac{1}{3}}x, & x > 0 \\ a^{x} + b, & x \leqslant 0 \end{cases}$ satisfies $f(0) = 2$ and $f(-1) = 3$. Find the value of $f(f(-3))$.

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