
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
For a sequence $\{a_{n}\}$ with $10$ terms, if $\{a_{n}\}$ satisfies $1\leqslant |a_{i+1}-a_{i}|\leqslant 2$ (where $i$ is a positive integer, $i\in \left[1,9\right]$), and $a_{1}=a_{10}\in \left[-1,0\right]$, let $k\in \{a_{n}|a_{n} \gt 0\}$. Find the maximum value of $k$.

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