
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
Given the following arrays, each composed of three numbers: $(1,2,3)$, $(2,4,6)$, $(3,8,11)$, $(4,16,20)$, $(5,32,37)$, ..., $(a\_n,b\_n,c\_n)$. If the sum of the first $n$ terms of the sequence $\{c\_n\}$ is denoted as $M\_n$, find the value of $M\_{10}$.

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