
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 fixed point $T(t,0)$ $(0 < t < 3)$, if the moving point $M$ with coordinates $(x,y)$ always satisfies the relation $\sqrt{(x-\sqrt{5})^2 + y^2} + \sqrt{(x+\sqrt{5})^2 + y^2} = 6$ during its motion, and the minimum value of $|MT|$ is $1$, then $t=$ ________.

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