
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 $f(x)=|x-a|$, if the solution set of the inequality $f(x) \leqslant 3$ is $\{|x|-1 \leqslant x \leqslant 5\}$.
(Ⅰ) Find the value of the real number $a$:
(Ⅱ) If the inequality $f(3x)+f(x+3) \geqslant m$ holds for all real numbers $x$, find the range of values for the real number $m$.

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