
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
On an island, there live three tribes: knights, who always tell the truth; liars, who always lie; and tricksters, who sometimes tell the truth and sometimes lie. At a round table sit 100 representatives of these tribes.

Each person at the table said two sentences: 1) "To my left sits a liar"; 2) "To my right sits a trickster". How many knights and liars are at the table if half of those present are tricksters?

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