
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
Alex is training to make  $\text{MOP}$ . Currently he will score a  $0$  on  $\text{the AMC,}\text{ the AIME,}\text{and the USAMO}$ . He can expend  $3$  units of effort to gain  $6$  points on the  $\text{AMC}$ ,  $7$  units of effort to gain  $10$  points on the  $\text{AIME}$ , and  $10$  units of effort to gain  $1$  point on the  $\text{USAMO}$ . He will need to get at least  $200$  points on  $\text{the AMC}$  and  $\text{AIME}$  combined and get at least  $21$  points on  $\text{the USAMO}$  to make  $\text{MOP}$ . What is the minimum amount of effort he can expend to make  $\text{MOP}$ ?

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