
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
Let $a$ be the price of an adult ticket. Given that the price of a child ticket is one-third the price of an adult ticket, the cost of a child ticket is $\frac{1}{3}a$. If the price for $3$ adult tickets and $5$ child tickets totals $21.00, determine the total cost of $7$ adult tickets and $4$ child tickets.

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