
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
A fraction \(\frac{b}{a}\) has its denominator decreased by 2, resulting in \(\frac{b}{a-2}\), which, when simplified, equals \(\frac{3}{4}\). If the original fraction's denominator is increased by 9, resulting in \(\frac{b}{a+9}\), which, when simplified, equals \(\frac{5}{7}\), then the value of \(\frac{b}{a} =\)?

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