
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]


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A student was taking a 150-point math test (divided into Part I and Part II) within 120 minutes. The scores obtained in Part I and Part II were P and Q respectively (in points), under the condition that at least 20 minutes were spent on each part. It was found that their relationship with the invested time m (in minutes) can be described by the empirical formulas $$P= \frac {1}{5}m+36$$ and $$Q=65+2 \sqrt {3m}$$.
(1) Find the function relationship and its domain between the total math score y (in points) and the time x (in minutes) invested in Part II;
(2) How should the time be allocated to achieve the highest score?

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