
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 three-row triangle structure is created using rods and connectors: the first row has 3 rods, the second has 6 rods, and the third has 9 rods, and so on, each row increasing by 3 rods. The connectors are used to join the ends of rods at every intersection point in accordance with the number of rows. However, the triangle structure now requires a stable base that consists of an additional row which has twice the amount of rods as the last top row and uses the same number of connectors as rods for stabilization. Determine the total number of pieces (rods and connectors) required to build a ten-row triangle with the stable base.

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