
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
A parallelogram $ABCD$ is formed by points $A$, $B$, $C$, and $D$. The lengths of $AB$ and $BC$ are 14 and 8, respectively. A point $P$ on side $AB$ is such that $AP:PB = 2:3$. Diagonal $AC$ is also drawn and is known to be 18. Point $Q$ is the midpoint of $AC$. Determine the distance from point $Q$ to line $BD$.

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