
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
On the extension of the side \( AB \) of rhombus \( ABCD \), a point \( M \) is taken beyond point \( B \) such that \( MD = MC \) and \(\angle MDC = \arctan \frac{8}{5} \). Find the ratio of the segments \( MA \) and \( MB \).

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