
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 $f(x)=|4x-a|+a^{2}-4a$ where $a \in \mathbb{R}$.

(1) When $a=1$, find the solution set of the inequality $-2 \leqslant f(x) \leqslant 4$.

(2) Let $g(x)=|x-1|$. If $f(x)-4g(x) \leqslant 6$ holds true for any $x \in \mathbb{R}$, find the range of values for the real number $a$.

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