
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
Let \\(m \in \mathbb{R}\\), and vectors \\(\mathbf{a}=(m+2,1)\\), \\(\mathbf{b}=(1,-2m)\\), given that \\(\mathbf{a} \perp \mathbf{b}\\), find \\(|\mathbf{a}+\mathbf{b}|=\\)            .

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