
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 that F₁ and F₂ are two foci of the ellipse $\frac{x^{2}}{12}$ + $\frac{y^{2}}{3}$ = 1, and point P is on the ellipse. If the midpoint of the segment PF₁ is on the y-axis, and PF₁ = tPF₂, then the value of t is _____.

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