
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 quadrilateral $ABCD$ with diagonals $AC$ and $BD$ intersecting at $O$, $BO=3$, $OD=9$, $AO=5$, $OC=2$, and $AB=7$. The length of $AD$ is:
A) $\sqrt{158}$  
B) $\sqrt{151}$  
C) $13$  
D) $12.5$  
E) $\sqrt{175}$

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