
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  $a_{n}$  be the area surrounded by the curves  $y=e^{-x}$  and the part of  $y=e^{-x}|\cos x|,\ (n-1)\pi \leq x\leq n\pi \ (n=1,\ 2,\ 3,\ \cdots).$  
Evaluate  $\lim_{n\to\infty}(a_{1}+a_{2}+\cdots+a_{n}).$ 

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