
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  $ k$  be a positive constant number. Denote  $ \alpha ,\ \beta \ (0<\beta <\alpha)$  the  $ x$  coordinates of the curve  $ C: y\equal{}kx^2\ (x\geq 0)$  and two lines  $ l: y\equal{}kx\plus{}\frac{1}{k},\ m: y\equal{}\minus{}kx\plus{}\frac{1}{k}$ .　Find the minimum area of the part bounded by the curve  $ C$  and two lines  $ l,\ m$ .

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