
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
Determine the integer \( x \) for which the following equation holds true:
\[ 1 \cdot 2023 + 2 \cdot 2022 + 3 \cdot 2021 + \dots + 2022 \cdot 2 + 2023 \cdot 1 = 2023 \cdot 1012 \cdot x. \]

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