
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 rectangle $ABCD$ with length 2 and height 1, an inscribed circle $\omega$ intersects $\overline{AB}$ at $Q$ (with $A$ at the top left corner and $B$ at the top right corner of the rectangle). Point $D$ is at the bottom left corner. Line segment $\overline{DQ}$ intersects circle $\omega$ again at a point $R$ different from $Q$. Find the length of $DR$.

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