
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
Define: \(\triangle a = a + (a + 1) + (a + 2) + \cdots + (2a - 2) + (2a - 1)\). For example: \(\triangle 5 = 5 + 6 + 7 + 8 + 9\). What is the result of \(\triangle 1 + \triangle 2 + \triangle 3 + \cdots + \triangle 19 + \triangle 20\)?

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