
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
 $a,b,c$  - are sides of triangle  $T$ . It is known, that if we increase any one  side by  $1$ , we get new
a) triangle
b)acute triangle

Find minimal possible area of triangle  $T$  in case of a) and in case b)

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