
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
The seats in a theater hall are divided into three categories according to their distance from the stage. "Category I" seats are the closest to the stage, make up two-fifths of the hall's capacity, and sell for 220 CZK. "Category II" seats make up the next two-fifths of the hall's capacity and sell for 200 CZK. The remaining "Category III" seats sell for 180 CZK. Before the pre-sale for the grand premiere, 150 tickets were given for free to invited guests. The tickets were distributed sequentially from the front seats of the hall to the back. All other tickets were then sold. If the free tickets had been distributed sequentially from the back seats to the front instead, the revenue would have been 4320 CZK higher. How many seats are in the hall?

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