
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 inequality

$$
\frac{\left(5 \cdot 2^{-\log _{x} 3}-2.5\right) \sqrt{2-\sqrt{\log _{x} 3+1}}}{1+\sqrt{\log _{x} 3+8}}>\frac{\left(2^{-\log _{x} 3}-0.5\right) \sqrt{2-\sqrt{\log _{x} 3+1}}}{\sqrt{\log _{x} 3+8}-3}
$$

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