
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

Solve the system of equations:

$$
\left\{\begin{aligned}
\log _{x}(y+1) & =4 \log _{x+2} \sqrt{y-1} \\
\log _{y-1}(x+2) & =\log _{x}\left(\frac{x^{3}}{y+1}\right)
\end{aligned}\right.
$$

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