
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 triangle $ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$. Let $\overrightarrow{m} = (\frac{a}{\sin(A+B)}, c - 2b)$ and $\overrightarrow{n} = (\sin 2C, 1)$, such that $\overrightarrow{m} \cdot \overrightarrow{n} = 0$.

1. Find the measure of angle $A$.
2. If $a = 1$, find the range of values for the perimeter of triangle $ABC$.

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