
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
Suppose \( r_{1}, r_{2}, r_{3} \) are the three 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 value of \( 7a - 9b \).

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