
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 sequence \(a_{n} = b[\sqrt{n+c}] + d\) is given, where the successive terms are
\[
1, 3, 3, 3, 5, 5, 5, 5, 5, \cdots
\]
In this sequence, each positive odd number \(m\) appears exactly \(m\) times consecutively. The integers \(b\), \(c\), and \(d\) are to be determined. Find the value of \(b+c+d\).

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