
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
Given a triangle with sides $a, b, c$, and an additional segment $d$. Let $a_{1}$ be the smaller of $a$ and $d$ (or their common value if they are equal), similarly let $b_{1}$ be the smaller of $b$ and $d$, and $c_{1}$ be the smaller of $c$ and $d$. Is it always possible to construct a triangle from the segments $a_{1}, b_{1}, c_{1}$?

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