
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 the piecewise function 
$$
f(x) = \begin{cases}
-log_{3}(x+1) & (x>6) \\
3^{x-6}-1 & (x\leq6)
\end{cases}
$$
satisfy $f(n) = -\frac{8}{9}$, calculate the value of $f(n+4)$.

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