
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
Suppose  $s,k,t\in \mathbb N$ . We've colored each natural number with one of the  $k$  colors, such that each color is used infinitely many times. We want to choose a subset  $\mathcal A$  of  $\mathbb N$  such that it has  $t$  disjoint monochromatic  $s$ -element subsets. What is the minimum number of elements of  $A$ ?

*Proposed by Navid Adham*

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