
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 vectors $\overrightarrow {m} = (\sqrt {3}\sin x, \sin x)$ and $\overrightarrow {n} = (\cos x, -\sin x)$, and $f(x) = 2\overrightarrow {m} \cdot \overrightarrow {n} + 2$.

(Ⅰ) Find the maximum value of the function $f(x)$, and the value of $x$ at which this maximum occurs;

(Ⅱ) Let the intersection of the graph of $f(x)$ with the y-axis, the first lowest point to the right of the y-axis, and the second intersection with the x-axis be denoted as $P$, $Q$, and $R$, respectively. Calculate the value of $\overrightarrow {QP} \cdot \overrightarrow {QR}$.

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