
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
In $\triangle ABC$, the side lengths opposite to internal angles A, B, and C are denoted as $a$, $b$, and $c$ respectively. It is known that the function $f(x) = \sin(2x - \frac {\pi}{6})$ satisfies the following condition: for any $x \in \mathbb{R}$, $f(x) \leq f(A)$ always holds.
  
(1) Determine the size of angle A.
  
(2) If $a = \sqrt{3}$, find the range of values for the length of the median AM from vertex A to side BC.

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