
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
Given square  $ BDEC$  with center  $ F$  is constructed externally to triangle  $ ABC$  such that  $\angle A = 90^{\circ}$, $\left|AB\right| = \sqrt{12}$, and $\left|AC\right| = 2$. If $\left[AF\right] \cap \left[BC\right] = \left\{G\right\}$, calculate $\left|BG\right|$.

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