
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 $M \leqslant a < b \leqslant c < d \leqslant M + 49$ and $ad = bc$, then $M$ is called a good number; otherwise, $M$ is called a bad number. Find the largest good number and the smallest bad number.

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