
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 coordinates of the vertices of triangle $OAB$ as $O(0,0)$, $A(2,9)$, $B(6,-3)$, point $P$ has an x-coordinate of $14$ and $OP=λPB$, and point $Q$ lies on edge $AB$ with $OQ \cdot AP=0$.

1. Find the value of the real number $λ$ and the coordinates of point $P$.
2. Find the coordinates of point $Q$.
3. If $R$ is a moving point on line segment $OQ$, find the range of values for $RO \cdot (RA+RB)$.

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