
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 $O$, suppose $BO=5$, $OD = 7$, $AO=9$, $OC=4$, and $AB=7$. The length of $AD$ is:
**A)** $15$
**B)** $\sqrt{210}$
**C)** $14$
**D)** $\sqrt{220}$
**E)** $13$

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