
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 $$\overrightarrow {m} = (\sin \omega x + \cos \omega x, \sqrt {3} \cos \omega x)$$, $$\overrightarrow {n} = (\cos \omega x - \sin \omega x, 2\sin \omega x)$$ ($\omega > 0$), and the function $f(x) = \overrightarrow {m} \cdot \overrightarrow {n}$, if the distance between two adjacent axes of symmetry of $f(x)$ is not less than $\frac {\pi}{2}$.
(1) Find the range of values for $\omega$;
(2) In $\triangle ABC$, where $a$, $b$, and $c$ are the sides opposite angles $A$, $B$, and $C$ respectively, and $a=2$, when $\omega$ is at its maximum, $f(A) = 1$, find the maximum area of $\triangle ABC$.

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