
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]


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Among any five nodes of a regular grid of hexagons, there will necessarily be two nodes such that the midpoint of the segment connecting them is also a node of this hexagonal grid. What is the minimum number of nodes of the hexagonal grid necessary to ensure that there will always be two nodes such that the midpoint of the segment joining them is also a node of this hexagonal grid?

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