
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
Consider a parameterized curve  $ C: x \equal{} e^{ \minus{} t}\cos t,\ y \equal{} e^{ \minus{} t}\sin t\ \left(0\leq t\leq \frac {\pi}{2}\right).$ 

(1) Find the length  $ L$  of  $ C$ .

(2) Find the area  $ S$  of the region bounded by  $ C$ , the  $ x$  axis and  $ y$  axis.

You may not use the formula  $ \boxed{\int_a^b \frac {1}{2}r(\theta)^2d\theta }$  here.

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