
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
Find $g(2)$ where the function $g(x)$ satisfies
\[ g(x) + g \left( \frac{2x + 1}{1 - 2x} \right) = 2x \]
for all $x \neq \frac{1}{2}$.

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