
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 function $f(x)=2\cos ^{2}x-(\sin x+\cos x)^{2}-2$. If there exist ${x_1},{x_2}∈[{0,\frac{{3π}}{4}}]$, such that the inequality $f(x_{1}) \lt k \lt f(x_{2})$ holds, then the integer value of $k$ can be ________ $(write one value only)$.

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