
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 $f(x) = |2x-4| + 1$.
- (I) Solve the inequality $f(x) > |x+1|$;
- (II) Let $a$ and $b$ be positive numbers satisfying $ab = a + b$. If the inequality $f(m+1) \leq a + 4b$ holds for any $a, b \in (0, +\infty)$, find the range of the real number $m$.

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