
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 collection of numbered indexed cards includes one card with a 1 written on it, two cards with a 2, and so forth up to $n$ cards showing an $n,$ for some positive integer $n$. In addition to these, there is one extra card showing the number $n+1$. Determine $n$, if the average value of a card in this collection is 2020.

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