
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 that $a > 0$, $b > 0$, $c > 0$, find the minimum value $m$ for the expression $\frac{1}{a^3} + \frac{1}{b^3} + \frac{1}{c^3} + 3abc$.  
(Ⅰ) Determine the value of $m$;  
(Ⅱ) Solve the inequality $|x+1| - 2x < m$ with respect to $x$.

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