
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 grasshopper starts at the origin in the coordinate plane and makes a sequence of hops. Each hop has length  $5$ , and after each hop the grasshopper is at a point whose coordinates are both integers; thus, there are  $12$  possible locations for the grasshopper after the first hop. What is the smallest number of hops needed for the grasshopper to reach the point  $(2021,2021)$ ?

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