
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
Adult tickets cost twice as much as child tickets, and senior tickets cost $1.50$ less than adult tickets. Given that the total cost for $6$ adult tickets, $5$ child tickets, and $3$ senior tickets is $40.50$, find the cost of $10$ adult tickets, $8$ child tickets, and $4$ senior tickets.

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