
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
For a positive integer \( M \), if there exist integers \( a, b, c, d \) such that
\[ M \leq a < b \leq c < d \leq M + 49 \]
and 
\[ a \cdot d = b \cdot c, \]
then \( M \) is called a good number; otherwise, \( M \) is called a bad number. Determine the largest good number and the smallest bad number.

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