
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 vertices $A$ and $C$ of triangle $ABC$, intersects side $AB$ at point $D$ and side $BC$ at point $E$. Find the angle $CDB$ if $AD=5$, $AC=2\sqrt{7}$, $BE=4$, and $BD:CE=3:2$.

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