
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 $f(x)=|x-a|-2$,
(1) If $a=1$, find the solution set of the inequality $f(x)+|2x-3| > 0$;
(2) If the inequality $f(x) > |x-3|$ has a solution, determine the range of values for the real number $a$.

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