
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
In Denver, CO, the temperature $T$ at any time $t$ hours past noon is given by the equation $T = -t^2 + 10t + 60$. On the same day, the atmospheric pressure $P$ in millibars is given by $P = 800 - 2t$. Find the smallest $t$ value at which the temperature is exactly 70 degrees.

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