
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 parabola C: y²=4x, point M(-1, 1), a line passing through the focus of C with a slope of k intersects C at points A and B. If $\overrightarrow {MA}\cdot \overrightarrow {MB}=0$, find the value of the real number k.

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