
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  $ A$  be the region :  $ \left\{(x,\ y)|x\geq 0,\ y\geq 0, \left(\frac{x}{a}\right)^{\frac{1}{2}}\plus{}\left(\frac{y}{1\minus{}a}\right)^{\frac{1}{2}}\leq 1\right\}$  for  $ 0<a<1.$ 

(1) Find the area of  $ A.$ 

(2) Find the maximum volume of the solid obtained by revolving  $ A$  around the  $ x$  axis.

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