
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 $f(x)=x\ln x-mx$ whose graph is tangent to the line $y=-1$.
(Ⅰ) Find the value of $m$, and determine the intervals of monotonicity for $f(x)$;
(Ⅱ) If $g(x)=ax^{3}$, let $h(x)=f(x)-g(x)$, discuss the number of zeros of the function $h(x)$.

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