
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 positive numbers \(a,b\) satisfying \(2ab=\dfrac{2a-b}{2a+3b},\) then the maximum value of \(b\) is \_\_\_\_\_

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