
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 $f(x) = |ax-1|$, the solution set of the inequality $f(x) \leq 3$ is $\{x | -1 \leq x \leq 2\}$.
(Ⅰ) Find the value of $a$;
(Ⅱ) If $\frac{f(x) + f(-x)}{3} < |k|$ has real solutions, find the range of values for the real number $k$.

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