
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 an acute triangle \( ABC \) where \(\angle A = 45^\circ\), the altitudes \( AA_1 \), \( BB_1 \), \( CC_1 \) are drawn. The angle bisector of \(\angle BAA_1\) intersects the line \( B_1A_1 \) at point \( D \), and the angle bisector of \(\angle CAA_1\) intersects the line \( C_1A_1 \) at point \( E \). Find the angle between the lines \( BD \) and \( CE \).

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