
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 $f(x) = |x - 1| - |2x - a|$,  
(1) When $a = 5$, find the solution set for the inequality $f(x) \geqslant 0$;  
(2) Let the solution set for the inequality $f(x) \geqslant 3$ be denoted by $A$, and assume that $5 \in A$ and $6 \notin A$. Determine the value of the integer $a$.

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