
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
Given triangle ABC, where sides $a$, $b$, and $c$ correspond to angles A, B, and C respectively, and $2c + a = 2b\cos{A}$.
(1) Find the measure of angle B.
(2) If $a = 5$, $c = 3$, and the midpoint of side AC is D, find the length of BD.

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