
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 $f(x) = |x|$;  
 (Ⅰ) Solve the inequality $f(2x) + f(x-2) > 3$;  
 (Ⅱ) For the function $g(x) = 3f(x) - f(x-t) (t \neq 0)$, if the area enclosed by the graph of $g(x)$ and the x-axis equals $3$, find the value of the real number $t$.

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