
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
There are 10 cards, labeled from 1 to 10. Three cards denoted by  $ a,\ b,\ c\ (a > b > c)$  are drawn from the cards at the same time.
Find the probability such that  $ \int_0^a (x^2 \minus{} 2bx \plus{} 3c)\ dx \equal{} 0$ .

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