
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 $\triangle ABC$, the length of the side opposite angle $A$ is equal to 2, the vector $\overrightarrow {m} = (2, 2\cos^2 \frac {B+C}{2}-1)$, and the vector $\overrightarrow {n} = (\sin \frac {A}{2}, -1)$.  
(1) Find the size of angle $A$ when the dot product $\overrightarrow {m} \cdot \overrightarrow {n}$ reaches its maximum value;  
(2) Under the condition of (1), find the maximum area of $\triangle ABC$.

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