
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 Proposition P: The equation $\frac {x^{2}}{t+2} + \frac {y^{2}}{t-10} = 1$ represents a hyperbola; and Proposition Q: $1-m < t < 1+m$ with $m>0$. If the negation of P is a sufficient but not necessary condition for the negation of Q, determine the range of values for the real number $m$.

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