
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
Insert three real numbers $a$, $b$, and $c$ between 1 and 16, so that the five numbers 1, $a$, $b$, $c$, 16 form a geometric sequence in order. Find the value of $a+c$.

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