
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
The water storage volume of two reservoirs, A and B, changes with time. The relationship between the water storage volume of reservoir A, $f(t)$ (in hundreds of tons), and time, $t$ (in hours), is given by $f(t)=2+\sin t$, where $t\in[0,12]$. The relationship between the water storage volume of reservoir B, $g(t)$ (in hundreds of tons), and time, $t$ (in hours), is given by $g(t)=5-|t-6|$, where $t\in[0,12]$. When do the sum of the water storage volumes of reservoirs A and B reach the maximum value? What is the maximum value? (Note: $\sin 6\approx-0.279$.)

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