
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 all positive integers  $N$  such that an  $N\times N$  board can be tiled using tiles of size  $5\times 5$  or  $1\times 3$ . 

Note: The tiles must completely cover all the board, with no overlappings.

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