
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 $M = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. A quadratic equation $x^2 - ax - b = 0$ is called a "quality equation" if $a, b \in M$ and the equation has at least one root $c \in M$. Find the number of "quality equations."

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