
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 functions $f(x)=|cx+a|+|cx-b|$ and $g(x)=|x-2|+c$.
(1) When $a=1$, $c=2$, $b=3$, solve the equation $f(x)-4=0$;
(2) When $c=1$, $b=1$, if for any $x\_1∈R$, there exists $x\_2∈R$ such that $g(x\_2)=f(x\_1)$ holds, find the range of values for the real number $a$.

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