
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,\ b$  are postive constant numbers.

(1) Differentiate  $ \ln (x\plus{}\sqrt{x^2\plus{}a})\ (x>0).$ 

(2) For  $ a\equal{}\frac{4b^2}{(e\minus{}e^{\minus{}1})^2}$ , evaluate  $ \int_0^b \frac{1}{\sqrt{x^2\plus{}a}}\ dx.$ 

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