
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 function $f(x)=2\sin(x+ \frac {π}{4})$, if for any two different numbers $x_1$, $x_2$ in the closed interval $[a, b]$, the inequality $$\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0$$ holds, write a closed interval that satisfies the condition.

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