
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
If \(a, b, c, d\) are positive real numbers such that \(\frac{5a + b}{5c + d} = \frac{6a + b}{6c + d}\) and \(\frac{7a + b}{7c + d} = 9\), calculate \(\frac{9a + b}{9c + d}\).

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