
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
Yura put  $2001$  coins of  $1$ ,  $2$  or  $3$  kopeykas in a row.  It turned out that between any two  $1$ -kopeyka coins there is at least one coin; between any two  $2$ -kopeykas coins there are at least two coins; and between any two  $3$ -kopeykas coins there are at least  $3$  coins.  How many  $3$ -koyepkas coins could Yura put?

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