
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 $\triangle ABC$, points $G$ and $H$ are on $\overline{AB}$ and $\overline{BC}$, respectively. If $\overline{AG}$ and $\overline{CH}$ intersect at $P$ such that $AP/PG=5$ and $CP/PH=3$, what is $BG/GH$?

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