
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 functions $f(x)=x^{3}-12x+3$ and $g(x)=3^{x}-m$.

(Ⅰ) Find the maximum and minimum values of $f(x)$ on the interval $[-1,5]$;

(Ⅱ) If for $\forall x_{1} \in [-1,5]$, $\exists x_{2} \in [0,2]$ such that $f(x_{1}) \geqslant g(x_{2})$ holds, find the minimum value of the real number $m$.

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