
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
For  $i=1,2,$  let  $T_i$  be a triangle with side length  $a_i,b_i,c_i,$  and area  $A_i.$  Suppose that  $a_1\le a_2, b_1\le b_2, c_1\le c_2,$  and that  $T_2$  is an acute triangle. Does it follow that  $A_1\le A_2$ ?

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