
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 $$\overrightarrow {m} = (\sin x, \cos x)$$, $$\overrightarrow {n} = (\sqrt {3}, -1)$$, and $$\overrightarrow {m} \cdot \overrightarrow {n} = 1$$, with $A$ being an angle.  
Find the range of the function $$f(x) = \cos 2x + 4\cos \sin x$$ ($x \in \mathbb{R}$).

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