
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
We will say that a rearrangement of the letters of a word has no *fixed letters* if, when the rearrangement is placed directly below the word, no column has the same letter repeated. For instance  $HBRATA$  is a rearragnement with no fixed letter of  $BHARAT$ . How many distinguishable rearrangements with no fixed letters does  $BHARAT$  have? (The two  $A$ s are considered identical.)

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