
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
To raise funds, an interactive game of "Guess the Poem from the Picture" was added. The organizer shows up to three pictures to each participant, with each picture corresponding to a poem. If a participant correctly identifies a line from the poem corresponding to a picture, it is considered as a correct answer for that picture. The organizer shows only one picture to the participant at a time. If the participant answers correctly, the next picture is shown; if the answer is incorrect, the game ends. For each correct answer, the participant can raise a fund for a charity organization, with the funds accumulating. It is known that a certain guest participating in this game has probabilities of correctly answering the first, second, and third pictures as $0.9$, $0.5$, and $0.4$, respectively. The corresponding amounts that can be raised for the charity organization are $1000$ yuan, $2000$ yuan, and $3000$ yuan. The correctness of each picture does not affect the others. The probability that this guest participates in this game and raises exactly $3000$ yuan for the charity fund is ____.

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