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

(1) If the function $f(x)$ has a maximum value, find the range of values for $a$;  
(2) If $a=1$, find the solution set for the inequality $f(x) > |2x-3|$.

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