
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 functions $f(x)=\sin({2x+\frac{π}{4}})$ and $g(x)=\sin({2x+\frac{{3π}}{4}})$, if for $0\leqslant x_{1} \lt x_{2}\leqslant t$, it always holds that $f(x_{1})-f(x_{2}) \lt g(x_{1})-g(x_{2})$, then the maximum value of the positive real number $t$ is ____.

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