
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 that G is the centroid of triangle ADE, P is any point inside (including the boundary) of triangle DEG, B and C are the trisection points on AD and AE respectively (closer to point A), and $\overrightarrow{AP}=α \overrightarrow{AB}+β \overrightarrow{AC}$ (where $α,β∈R$), find the range of $α+ \dfrac {1}{2}β$.

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