
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: 
\[
\frac{1+\frac{1+\frac{1+x}{1-3 x}}{1-3 \cdot \frac{1+x}{1-3 x}}}{1-3 \cdot \frac{1+\frac{1+x}{1-3 x}}{1-3 \cdot \frac{1+x}{1-3 x}}} < \frac{1-3 \cdot \frac{1+\frac{1+x}{1-3 x}}{1-3 \cdot \frac{1+x}{1-3 x}}}{1+\frac{1+\frac{1+x}{1-3 x}}{1-3 \cdot \frac{1+x}{1-3 x}}}
\]

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