
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
This pattern is constructed using matchsticks. If the pattern begins with five matchsticks and for each subsequent stage, three matchsticks are added, along with an extra matchstick added after every fifth stage, how many matchsticks are required to form the $20^{th}$ stage?

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