
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 function f(x) = sin(ωx + $\frac{π}{6}$) + $\frac{1}{2}$ (ω > 0), points P, Q, and R are three adjacent intersection points of the line y = m (m > 0) and the graph of function f(x) from left to right. Also, 2|PQ| = |QR| = $\frac{2π}{3}$. Find the value of ω + m.

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