
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 triangle \(BCD\), \(BC = 3\) and \(CD = 5\). From vertex \(C\), segment \(CM\) is drawn where \(M \in BD\), and \(\angle BCM = 45^\circ\) and \(\angle MCD = 60^\circ\).

a) In what ratio does point \(M\) divide side \(BD\)?

b) Calculate the lengths of segments \(BM\) and \(MD\).

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