
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
Let \(r_1, r_2, r_3\) be the roots of the real-coefficient equation \(x^3 - x^2 + ax - b = 0\), where \(0 < r_i < 1\) for \(i=1,2,3\). Find the maximum possible value of \(7a - 9b\).

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