
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
A fly and $\mathrm{k}$ spiders are moving on a $2019 \times 2019$ grid. On its turn, the fly can move by 1 square and the $k$ spiders can each move by 1 square. What is the minimal $k$ for which the spiders are guaranteed to catch the fly?

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