
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
Selected Exercise $(4-5)$: Inequality Lecture

Given the function $f(x) = |2x - a| + a$.

$(1)$ When $a = 3$, find the solution set of the inequality $f(x) \leqslant 6$.

$(2)$ Let $g(x) = |2x - 3|$. For all $x \in \mathbb{R}$, if $f(x) + g(x) \geqslant 5$, find the range of values for $a$.

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