
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
We want to cover totally a square(side is equal to  $k$  integer and  $k>1$ ) with this rectangles: $1$  rectangle ( $1\times 1$ ),  $2$  rectangles ( $2\times 1$ ),  $4$  rectangles ( $3\times 1$ ),....,  $2^n$  rectangles ( $n + 1 \times 1$ ), such that the rectangles can't overlap and don't exceed the limits of square.
Find all  $k$ , such that this is possible and for each  $k$  found you have to draw a solution

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