
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 $f(x)=\sin ^{2}(2x- \frac {π}{4})-2t\cdot\sin (2x- \frac {π}{4})+t^{2}-6t+1(x\in\ [ \frac {π}{24}, \frac {π}{2}])$, its minimum value is $g(t)$.

1. Find the expression for $g(t)$;
2. When $- \frac {1}{2}\leqslant t\leqslant 1$, in order to make the equation $g(t)=kt$ have one real root, find the range of the real number $k$.

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