
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 $f(x) = -|x-2|$ and $g(x) = -|x-3| + m$,

(1) If the graph of function $f(x)$ is always above the graph of function $g(x)$, find the range of $m$.  
(2) Solve the inequality $f(x) + a - 1 > 0$, where $a \in \mathbb{R}$.

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