
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
For every \\(x_1 \in \mathbb{R}\\), there exists \\(x_2 \in [3,4]\\) such that the inequality \\(x_1^2 + x_1x_2 + x_2^2 \geqslant 2x_1 + mx_2 + 3\\) holds. Then, the range of the real number \\(m\\) is \_\_\_\_\_\_\_\_\_\_.

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