
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 system, the vertices of triangle $ABC$ are: $A(0, 4)$, $B(3, 0)$, and $C(c, 6)$. The area of the triangle is 7. What is the value of $c$, if it is known that $0 < c < 3$?

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