
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 the coordinate plane, let  $A = (-8, 0)$ ,  $B = (8, 0)$ , and  $C = (t, 6)$ .  What is the maximum value of  $\sin m\angle CAB \cdot \sin m\angle CBA$ , over all real numbers  $t$ ?

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