
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
A cubic function  $ y \equal{} ax^3 \plus{} bx^2 \plus{} cx \plus{} d\ (a\neq 0)$  touches a line  $ y \equal{} px \plus{} q$  at  $ x \equal{} \alpha$  and intersects  $ x \equal{} \beta \ (\alpha \neq \beta)$ .
Find the area of the region bounded by these graphs in terms of  $ a,\ \alpha ,\  \beta$ .

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