
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
To celebrate the Chinese football team's first entry into the World Cup, Pinghu Sports Equipment Factory donated a batch of footballs to the Wuxia Middle School football team. If each team member takes one football, there are 9 balls short; if every two members share one football, there are 9 balls left. How many footballs are there in total?  
After receiving the football, Xiao Ming was very happy and started to carefully study the black and white patches on the football. He found that the black patches are regular pentagons, the white patches are regular hexagons, and they are alternately inlaid on the sphere. There are 12 black patches in total. How many white patches are there?

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