
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
In the  $ xy$  plane, the line  $ l$  touches to 2 parabolas  $ y\equal{}x^2\plus{}ax,\ y\equal{}x^2\minus{}2ax$ , where  $ a$  is positive constant.

(1) Find the equation of  $ l$ .

(2) Find the area  $ S$  bounded by the parabolas and the tangent line  $ l$ .

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