
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 a function $f(x) = ax^3 + bx^2 + cx + d$ ($a, b, c, d \in \mathbb{R}$) defined on $\mathbb{R}$ whose graph is symmetrical with respect to the origin and attains its minimum value of $-2$ at $x = 1$.

(Ⅰ) Determine the interval where $f(x)$ is monotonically increasing;

(Ⅱ) Solve the inequality $f(x) > 5mx^2 - (4m^2 + 3)x$ for $x$ where $m \in \mathbb{R}$.

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