
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
Given the function $f(x) = \frac{a}{x} + \ln x - n$ ($a > 0$), where $n = \int_{0}^{\frac{\pi}{2}} (2\sin \frac{t}{2}\cos \frac{t}{2})dt$. If the function $f(x)$ has a root within its domain, then the range of values for the real number $a$ is \_\_\_\_\_\_.

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