
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 $\triangle DEF$, where $DE = 105$, and $DF = 110$. A circle with center $D$ and radius $DE$ intersects $\overline{EF}$ at points $E$ and $Y$. Both $\overline{EY}$ and $\overline{FY}$ have integer lengths. What is $EF$?
**A)** 25  
**B)** 35  
**C)** 43  
**D)** 110  
**E)** 125

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