
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
Vectors $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are both unit vectors, given by $\overrightarrow{OA} = \{p, q, 0\}$ and $\overrightarrow{OB} = \{r, s, 0\}$. Both vectors form a $45^\circ$ angle with $\overrightarrow{OC} = \{1, 1, 1\}$.
1. Find the values of $p + q$ and $pq$.
2. Determine the measure of the acute angle $\angle AOB$.

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