
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 \( ABC \), \( AB = 4 \) and \( BC = 5 \). From vertex \( B \), a segment \( BM \) (where \( M \in AC \)) is drawn, such that \(\angle ABM = 45^\circ\) and \(\angle MBC = 30^\circ\).

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

b) Calculate the lengths of segments \( AM \) and \( MC \).

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