
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
Ancient Greek mathematicians associated natural numbers with polygons in the following manner:

Triangular numbers: \(1, 3, 6, 10, 15\)

Square numbers: \(1, 4, 9, 16, 25\)

Pentagonal numbers: \(1, 5, 12, 22, 35\)

Hexagonal numbers: \(1, 6, 15, 28, 45\)

Following the above sequence, the 6th pentagonal number is \(\_\_\_\_\_\_ \).

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