
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 the function \( f(x)=\frac{x^{2}+x+16}{x} \) where \( 2 \leqslant x \leqslant a \) and the real number \( a > 2 \). If the range of \( f(x) \) is \([9, 11]\), then find the range of values for \( a \).

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