
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 functions $f(x) = |x-1|$ and $g(x) = 2|x-a|$, where $a \in \mathbb{R}$.
(1) If $a=2$, find the solution set of the inequality $f(x) - g(x) \leq x - 3$.
(2) If for every $m > 1$, there exists an $x_0 \in \mathbb{R}$ such that $f(x) + g(x) \leq \frac {m^{2}+m+4}{m-1}$ holds, find the range of values for $a$.

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