
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
Calculate the value of $x$ for which the following equation holds true:
\[1 \cdot 2021 + 2 \cdot 2020 + 3 \cdot 2019 + \dots + 2020 \cdot 2 + 2021 \cdot 1 = 2021 \cdot 1011 \cdot x.\]

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