
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 a sequence $\{a_{n}\}$ that satisfies: $a_{1}=1$, $a_{n+1}-a_{n}\in \{a_{1}$, $a_{2}$, $\ldots $, $a_{n}\}(n\in N^{*})$, let the sum of the first $n$ terms of the sequence $\{a_{n}\}$ be $S_{n}$. If for all sequences $\{a_{n}\}$ that satisfy the conditions, the maximum value of $S_{10}$ is $M$, and the minimum value is $m$, then $M+m=$____.

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