
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 inequalities:

$$\left\{\begin{array}{l}(x-1) \lg 2+\lg \left(2^{x+1}+1\right)<\lg \left(7 \cdot 2^{x}+12\right) \\ \log _{x}(x+2)>2\end{array}\right.$$

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