
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
Theorem: \( |m_{3}| \leq 3, |m_{4}| \leq 5, |m_{5}| \leq 7, |m_{6}| \leq 9, |m_{7}| \leq 12, |m_{8}| \leq 14, |m_{9}| \leq 16, |m_{10}| \leq 19 \), and all numbers cannot decrease.

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