
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 $f(x)=x+ \frac{a}{x}+b(x\neq 0)$, where $a, b \in R$. If for any $a \in [\frac{1}{2}, 2]$, the inequality $f(x) \leqslant 10$ always holds for $x \in [\frac{1}{4}, 1]$, then the range of values for $b$ is $\_\_\_\_\_\_\_\_$.

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