
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
Given that Xiao Gang simplifies $\frac{2a}{{a}^{2}-{b}^{2}}-\frac{1}{M}$ to $\frac{1}{a-b}$, while the copied $M$ is greater than the original $M$ by $2b$, simplify the original expression.

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