
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
On the sides \( AB \) and \( AC \) of triangle \( ABC \), points \( X \) and \( Y \) are chosen, respectively, such that \(\angle AYB = \angle AXC = 134^\circ\). Point \( M \) is marked on ray \( YB \) beyond point \( B \), and point \( N \) is marked on ray \( XC \) beyond point \( C \). It turned out that \( MB = AC \) and \( AB = CN \). Find \(\angle MAN\).

Answer: \( 46^\circ \).

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