
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 $\triangle DEF$, side $e = 2$, side $f = 2$, and side $d > 2\sqrt{2}$. Let $y$ be the largest number such that the angle opposite to side $d$, in degrees, exceeds $y$. Determine the value of $y$.
A) $90^{\circ}$
B) $105^{\circ}$
C) $120^{\circ}$
D) $135^{\circ}$
E) $150^{\circ}$

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