
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 that $\overrightarrow{a}$ and $\overrightarrow{b}$ are two mutually perpendicular unit vectors, and $|\overrightarrow{c}| = 13$, $\overrightarrow{c} \cdot \overrightarrow{a} = 3$, $\overrightarrow{c} \cdot \overrightarrow{b} = 4$, find the minimum value of $|\overrightarrow{c} - t_1\overrightarrow{a} - t_2\overrightarrow{b}|$ for any real numbers $t_1$ and $t_2$.

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