
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
A company found that, disregarding other factors, the monthly profit $y$ (in ten thousand yuan) and the month number have the following functional relationship when analyzing its business performance in 2012: $f(x) = \begin{cases} 12x+28 & (1\leq x \leq 6, x \in \mathbb{N}^{*}) \\ 200-14x & (6 < x \leq 12, x \in \mathbb{N}^{*}) \end{cases}$  
(Ⅰ) What is the profit in May?  
(Ⅱ) In which month of 2012 did the company achieve the highest monthly profit? What is the maximum profit?

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