
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
Determine the value of $a - b$ if the equation
\[
\frac{a}{2^x-2} + \frac{b}{2^x+3} = \frac{5 \cdot 2^x + 4}{(2^x-2)(2^x+3)}
\]
is an identity for positive rational values of $x$.
A) $\frac{1}{5}$  
B) $\frac{2}{5}$  
C) $\frac{3}{5}$  
D) $\frac{4}{5}$  
E) $\frac{5}{5}$

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