
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
What is the maximum possible area of a triangle with sides \(a\), \(b\), and \(c\) that fall within the following ranges:

\[ 0 \leq a \leq 1, \quad 1 \leq b \leq 2, \quad 2 \leq c \leq 3? \]

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