
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 $f(x)=|x-1|+|x-t|$, where $t\in\mathbb{R}$,
(1) When $t=2$, find the solution set for the inequality $f(x) > 2$;
(2) If for any $t\in[1,2]$ and $x\in[-1,3]$, the inequality $f(x)\geq a+x$ always holds, find the range of values for the real number $a$.

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