
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 circle passes through the points  $A,C$  of triangle  $ABC$  intersects with the sides  $AB,BC$  at points  $D,E$  respectively. Let  $ \frac{BD}{CE}=\frac{3}{2}$ ,  $BE=4$ ,  $AD=5$  and  $AC=2\sqrt{7} $ .
Find the angle  $ \angle BDC$ .

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