
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
\[
\left(\frac{b x+4+\frac{4}{b x}}{2 b+\left(b^{2}-4\right) x-2 b x^{2}}+\frac{\left(4 x^{2}-b^{2}\right) \cdot \frac{1}{b}}{(b+2 x)^{2}-8 b x}\right) \cdot \frac{b x}{2}
\]

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