
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
A function $f(x)$ defined on $[1,+\infty)$ satisfies the following conditions: (1) $f(2x)=mf(x)$, where $m$ is a positive constant, and (2) when $2\leqslant x\leqslant 4$, $f(x)=1-|x-3|$. If all the maximum points of the function lie on the same straight line, then $m$ equals \_\_\_\_\_\_.

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