
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
A rectangle is divided into four triangles as shown in the picture. We measured all the internal angles in these triangles and obtained the following values: \(15^{\circ}, 20^{\circ}, 20^{\circ}, 50^{\circ}, 55^{\circ}\), \(70^{\circ}, 75^{\circ}, 75^{\circ}, 90^{\circ}, 90^{\circ}, 130^{\circ}\) and one more value that we forgot to record. Find the missing value and state which angle it is, knowing that the line segment \(BE\) is longer than the line segment \(FC\). (Note that the picture may be inaccurate, and it is not advisable to measure.) 

(S. Bednářová)

![image](https://cdn.mathpix.com/cropped/2024_04_17_fa77236f1bc7a0516474g-1.jpg?height=462&width=1131&top_left_y=1962&top_left_x=494)

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