
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
In the right rectangular prism $ABCD-A_1B_1C_1D_1$, $O$ is the center of the base $ABCD$, $P$ is the midpoint of $DD_1$, and $Q$ is a point on $CC_1$. Determine the position of point $Q$ such that the plane $D_1BQ$ is parallel to the plane $PAO$.

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