
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
For any real number $x$, the inequality $|x+6|+|x-1|\geqslant m$ always holds.

(I) Find the range of $m$;

(II) When $m$ takes the maximum value, solve the inequality $|x-4|-3x\leqslant 2m-9$ with respect to $x$.

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