
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  $P(x,\ y)\ (x>0,\ y>0)$  be a point on the curve  $C: x^2-y^2=1$ . If  $x=\frac{e^u+e^{-u}}{2}\ (u\geq 0)$ , then find the area bounded by the line  $OP$ , the  $x$  axis and the curve  $C$  in terms of  $u$ .

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