
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 that $(x+1)^{10}=a\_1+a\_2x+a\_3x^{2}+…+a_{11}x^{10}$. If the sequence $a\_1$, $a\_2$, $a\_3$, $…$, $a\_k (1≤k≤11, k∈Z)$ is a strictly increasing sequence, then the maximum value of $k$ is _____.

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