
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
Someone performs the following transformations on the inequality:

$$
\begin{aligned}
& \frac{1}{4}>\frac{1}{8} ; \quad\left(\frac{1}{2}\right)^{2}>\left(\frac{1}{2}\right)^{3} \\
& 2 \lg \frac{1}{2}>3 \lg \frac{1}{2}, \quad \text { therefore } \quad 2>3
\end{aligned}
$$

Where is the mistake?

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