
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 general term of the sequence is given by \( a_{n} = b[\sqrt{n+c}] + d \). The sequence is calculated successively as follows:
\[ 1, 3, 3, 3, 5, 5, 5, 5, 5, \cdots \]

In this sequence, each positive odd number \( m \) appears exactly \( m \) times consecutively. Determine the value of \( b + c + d \), where \( b, c, \) and \( d \) are integers to be determined.

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