
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 recent years, live streaming e-commerce has gradually become an emerging marketing model, bringing new growth points to the e-commerce industry. At the beginning of the first year, a certain live streaming platform had an initial capital of 5 million yuan. Due to the participation of some well-known hosts, the platform's annual average capital growth rate can reach 40%. At the end of each year, operating costs of $a$ million yuan are deducted, and the remaining funds are reinvested in the live streaming platform.  
$(1)$ If $a=100$, how many million yuan will the live streaming platform have at the end of the third year after deducting operating costs?  
$(2)$ How much should the maximum annual operating cost be controlled at most, in order for the live streaming platform to reach 3000 million yuan at the end of the sixth year after deducting operating costs? (Give the result accurate to 0.1 million yuan)

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