
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 vectors $\overrightarrow{AB} = (1, 2\cos \theta)$ and $\overrightarrow{BC} = (m, -4)$, where $\theta \in (-\frac{\pi}{2}, \frac{\pi}{2})$.
1. If $m = -4$ and points $A$, $B$, and $C$ are collinear, find the value of $\theta$.
2. If for any $m \in [-1, 0]$, the dot product $\overrightarrow{AC} \cdot \overrightarrow{BC} \leq 10$ always holds true, find the maximum value of $\sin(\theta - \frac{\pi}{2})$.

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