
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
Find the smallest integer  $n$  such that an  $n\times n$  square can be partitioned into  $40\times 40$  and  $49\times 49$  squares, with both types of squares present in the partition, if
a)  $40|n$ ; b)  $49|n$ ; c)  $n\in \mathbb N$ .

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