
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 $\sin\alpha - 2\cos\alpha = 0$, find the value of $$\frac {\sin\alpha + \cos\alpha}{2\sin\alpha - \cos\alpha}.$$  
(2) If $f(x) = 3\cos x - \sin^2 x + 1$, and $f(x) \geq a - 3$ always holds, find the range of $a$.

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