
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  quartic funtion  $ y \equal{} ax^4 \plus{} bx^3 \plus{} cx^2 \plus{} dx\plus{}e\ (a\neq 0)$  touches the line  $ y \equal{} px \plus{} q$  at  $ x \equal{} \alpha ,\ \beta \ (\alpha < \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}
user