
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 corresponding interval \[a, b\] obtained from the mapping $f: x \rightarrow 2x + m$ for the interval \[0, m\] is given. If the length of the interval \[a, b\] is 5 units greater than the length of the interval \[0, m\], then find the value of $m$. (The length of the interval \[a, b\] is defined as $b-a$).

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