
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 $f(x) = |x+1| + |2x+m|$.
(I) When $m=-3$, find the solution set of the inequality $f(x) \leq 6$.
(II) Let $M$ be the solution set of the inequality $f(x) \leq |2x-4|$ with respect to $x$, and $[-1, \frac{1}{2}] \subseteq M$. Find the range of values for the real number $m$.

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