
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
Consider the dark hexagon in an array of regular hexagonal cells. The first ring around this central hexagon contains 6 smaller regular hexagons. Each subsequent ring around the center adds hexagons in such a way that the number of hexagons in each ring grows in the series $6n$, where $n$ is the ring number. Calculate the number of hexagons in the $50^{th}$ ring.

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