
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 a triangle  $ABC$ , the median  $AD$  divides  $\angle{BAC}$  in the ratio  $1:2$ . Extend  $AD$  to  $E$  such that  $EB$  is perpendicular  $AB$ . Given that  $BE=3,BA=4$ , find the integer nearest to  $BC^2$ .

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