
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
(1) Given $\tan\beta= \frac {1}{2}$, find the value of $\sin^2\beta-3\sin\beta\cos\beta+4\cos^2\beta$.  
(2) Find the domain of the function: $y= \sqrt {-2\cos^2x+3\cos x-1}+\log_{10}(36-x^2)$.

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