
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 an isosceles triangle ABC, where the base points A and B are on the right branch of the hyperbola $\frac {x^{2}}{6}- \frac {y^{2}}{3}$=1, and the vertex C is on the x-axis. If AB is not perpendicular to the x-axis, find the range of the x-coordinate t of vertex C.

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