
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
Five cards have the numbers \(101, 102, 103, 104, \text{ and } 105\) on their fronts. On the reverse, each card has a statement printed as follows:
- 101: The statement on card 102 is false
- 102: Exactly two of these cards have true statements
- 103: Four of these cards have false statements
- 104: The statement on card 101 is false
- 105: The statements on cards 102 and 104 are both false

What is the total of the numbers shown on the front of the cards with TRUE statements?

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