
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 triangle $ABC,$ points $P$ and $Q$ are on $\overline{AB}$ and $\overline{AC},$ respectively, and the angle bisector $\overline{AU}$ intersects $\overline{PQ}$ at point $R.$ If $AP = 2,$ $PB = 6,$ $AQ = 4,$ and $QC = 5,$ compute the ratio $\frac{AR}{AU}.$

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