
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 $f(x) = x + \frac{a}{x} + b$ ($x \neq 0$, $a, b \in \mathbb{R}$), if for any $a \in \left[\frac{1}{2}, 2\right]$, the inequality $f(x) \leq 10$ always holds for $x \in \left[\frac{1}{4}, 1\right]$, then the range of values for $b$ is _______.

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