
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 the vectors $\overrightarrow {p} =(\sin A, \cos A)$ and $\overrightarrow {q} = (\sqrt {3}\cos A, -\cos A)$ (where $\overrightarrow {q} \neq \overrightarrow {0}$),
1. If $0<A<\frac{\pi}{2}$, the equation $\overrightarrow {p} \cdot \overrightarrow {q} = t - \frac{1}{2} \ (t \in \mathbb{R})$ has exactly one solution, find the range of $t$;
2. Let $\triangle ABC$ have interior angles $A$, $B$, and $C$, with opposite sides $a$, $b$, and $c$ respectively, and let $a = \frac{\sqrt{3}}{2}$. If $\overrightarrow {p} \parallel \overrightarrow {q}$, find the range for the sum of $b$ and $c$.

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