
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
For the positive constant number  $ a$ , let  $ D$  be the part surrounded by the curve  $ \sqrt{x}\plus{}\sqrt{y}\equal{}\sqrt{a}$  and  the line  $ x\plus{}y\equal{}a$ .

(1) Draw the outline of  $ D$  and find the area.

(2) Find the volume of the solid by rotating  $ D$  about the line  $ x\plus{}y\equal{}a$  as the rotation axis.

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