
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  $a$ ,  $b$ ,  $c$  and  $d$  so that:
\[ M \leq a < b \leq c < d \leq M+49, \qquad ad=bc \]
then we call  $M$  a GOOD number, if not then  $M$  is BAD. Please find the greatest GOOD number and the smallest BAD number.

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