
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 sides opposite to angles A, B, and C are denoted by $a$, $b$, and $c$ respectively. It is given that vectors $\overrightarrow{m} = ((b+c)^2, -1)$ and $\overrightarrow{n} = (1, a^2+bc)$, and $\overrightarrow{m} \cdot \overrightarrow{n} = 0$.
(1) Determine the magnitude of angle A.
(2) If $a=3$, find the range of possible values for the perimeter of $\triangle ABC$.

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