
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 the function $f(x) = |x-a| + 3x$, where $a > 0$.
(Ⅰ) When $a=1$, find the solution set for the inequality $f(x) \geqslant 3x+2$.
(Ⅱ) If the solution set for the inequality $f(x) \leqslant 0$ is $\{x|x \leqslant -1\}$, find the value of $a$.

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